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Re: pi(x) - pi(x/7) > sqrt(x)

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  • John
    David thanks, Sorry I left off the Harold in Harold N. Shapiro. John W. Nicholson
    Message 1 of 4 , Jul 14, 2010
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      David thanks,

      Sorry I left off the "Harold" in Harold N. Shapiro.

      John W. Nicholson


      --- In primenumbers@yahoogroups.com, "djbroadhurst" <d.broadhurst@...> wrote:
      >
      >
      >
      > --- In primenumbers@yahoogroups.com,
      > "John W. Nicholson" <reddwarf2956@> wrote:
      >
      > > pi(x) - pi(x/7) > sqrt(x) proved by N. Shapiro
      >
      > A proof, for integer x > 2, was given by Harold Shapiro
      > in 1953 and may be found here:
      >
      > http://tinyurl.com/3yycvms
      >
      > The inequality is true by inspection for 2 < x < 10590
      > and for larger x follows from a stronger result by
      > Ramanujan, given in Eq. (3.2) of Shapiro's paper.
      >
      > David
      >
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